Methods and apparatuses for measuring the resistivity of drilling mud in a borehole

ABSTRACT

A method of measuring the resistivity of drilling mud in a borehole passing through a terrestrial formation includes the steps of a) inserting a sonde into the borehole, the sonde having an elongate body provided with at least one annular current electrode (A 0 , A′ 0 ) and at least two annular guard electrodes (A, A′, A 1 , A′ 1 , A 2 , A′ 2 ) situated on either side of the annular current electrode; b) performing computed focusing to simulate an operating mode in which at least one current I 0  is emitted into the surrounding formation from the annular current electrode, the current I 0  being focused in the formation by emitting two currents I 1  and I′ 1  from the two annular guard electrodes situated on either side of the annular current electrode; and c) producing a signal representative of the resistivity R m  of the drilling mud from the simulated operating mode. Apparatus for measuring the resistivity of drilling mud in a borehole includes the sonde, and electronic circuitry for performing computed focusing and computing a signal representative of the resistivity R m  of the drilling mud on the basis of the computed focusing.

The present application is a division of application Ser. No.08/733,583, filed Oct. 18, 1996, now U.S. Pat. No. 6,046,593.

BACKGROUND OF THE INVENTION Technical Field and Prior Art

The present invention relates to the field of measurement tools, e.g.,suitable for use in equipment for oil prospecting and production.

More specifically, after a well has been bored, that type of activityrequires sondes or sensors, in particular electrical or electromagneticsondes or sensors to be inserted into the hole to enable measurements tobe performed serving to characterize, amongst others, which fluids arepresent in the terrain and layers around the borehole, and also the dipof said layers. The term “logging” is used to designate any continuousrecording as a function of depth of variations in a given characteristicof the formations around a borehole.

One of the characteristics that it is important to know in a borehole isthe resistivity of the drilling mud used. The resistivity of the mud isa parameter that is used, in particular, to correct measurementsrelating to other characteristics of the surrounding formations. Inorder to discover this mud resistivity, various approaches are alreadyknown.

In a first approach, mud resistivity is measured by a device thatrequires additional equipment on the tool already used for measuring thecharacteristics of the formation, which additional equipment may be, forexample, of the AMS type (described in document EP013 224). Thattechnique gives rise to additional costs and to apparatus that is ofgreater bulk.

In another technique, the resistivity of the mud is measured at thesurface from a fluid sample. Extrapolation then makes it possible totake account of temperature dependence relative to downhole conditionsby measuring the temperature down hole. The accuracy obtained is oftenunsatisfactory, essentially for the following two reasons:

difficultly in obtaining an accurate measurement of the temperaturedownhole; and

the characteristics of the fluid in the borehole can change with depth,in which case the sample available on the surface is no longerrepresentative.

SUMMARY OF THE INVENTION

An object of the invention is to provide a novel method and novelapparatus enabling a measurement to be obtained of the resistivity ofthe mud in a borehole, without requiring additional specific apparatusto be implemented, but capable of making use of electrode structuresthat already exist. In addition, the new method and the new apparatusmust be capable of measuring the resistivity of the mud in situ, withoutit being necessary to take samples for subsequent analysis on thesurface. Finally, it is desirable to find a method and an apparatus thatenable measurements to be made on the mud without requiring any priormeasurement of the azimuth resistivity of the surrounding formations,and which is relatively insensitive to the influence of the diameter ofthe borehole.

In a first aspect of the invention, the invention provides a method ofmeasuring the resistivity R_(m) of a drilling mud inside a boreholepassing through a terrestrial formation, the method comprising:

inserting a sonde into the borehole, the sonde having an elongate bodyprovided with at least one annular current electrode and at least twoannular guard electrodes situated on either side of the annular currentelectrode;

emitting at least one current I₀ into the surrounding formation from theannular current electrode;

focusing the current I₀ in the formation by emitting two currents I₁ andI′₁ from the annular guard electrodes situated on either side of theannular current electrode; and

producing a signal in response to the emitted current I₀, which signalis representative of the resistivity R_(m) of the drilling mud.

This method is a method of measuring the resistivity of the mud in situ.It does not require any prior knowledge of the azimuth resistivity ofthe surrounding formations. In addition, it is relatively insensitive tothe effects due to variations in the dimensions of the borehole,particularly when the borehole diameter is relatively large. Finally, itshould be observed that mud resistivity is measured by emitting currentinto the surrounding formation, and not by emitting surface current intothe mud.

A signal may be produced that is representative of a voltage inducedthrough the borehole mud by the current I₀ circulating through said mudand the formation.

The sonde may include a single annular current electrode, first andsecond pairs of annular electrodes referred to as electrodes formeasuring voltage in the borehole mud, each pair being disposed oneither side of the annular current electrode, the resistivity R_(m)being deduced from the ratio (V₁−V₃)/I₀ in which V₁ and V₃ are the meanpotentials of the two pairs of electrodes for measuring voltage in thedrilling mud.

In another embodiment, the sonde may include:

two annular current electrodes respectively emitting a current I₀ and acurrent I′₀ into the surrounding formation; and

an annular potential-measuring electrode situated between the twocurrent electrodes or else an array of azimuth electrodes situatedbetween the two annular current electrodes.

This embodiment is particularly well adapted to enabling the method tobe implemented using electrode structures that already exist.

The invention also provides an apparatus for measuring the resistivityof drilling mud in a borehole passing through a terrestrial formation,the apparatus comprising:

a sonde having an elongate body provided with at least one annularcurrent electrode and at least two annular guard electrodes situated oneither side of the annular current electrode;

means for emitting at least one current I₀ into the surroundingformation from the annular current electrode;

means for focusing the current I₀ in the formation by emitting twocurrents I₁ and I′1 from the two annular guard electrodes situated oneither side of the annular current electrode; and

means for producing a signal in response to the emission of the currentI₀, said signal being representative of the resistivity R_(m) of thedrilling mud.

This apparatus is associated with the same advantages as those specifiedabove with reference to the first method of measurement of theinvention: it enables measurements to be performed in situ, and it doesnot require prior knowledge of azimuth resistivities.

The apparatus may include means for producing a signal representative ofa voltage induced through a drilling mud by the current I₀, because ofthe current flowing through the mud and through the formation.

Thus, the sonde may include a single annular current electrode, firstand second pairs of annular electrodes for measuring voltage in thedrilling mud, each pair being disposed on either side of the annularcurrent electrode, the means for producing a signal representative ofthe resistivity R_(m) enabling R_(m) to be deduced from the ratio(V₁−V₃)/I₀, where V₁ and V₃ are the mean potentials of the two pairs ofelectrodes for measuring voltage in the drilling mud.

In another aspect, the same apparatus may be such that the sondeincludes:

two annular current electrodes;

means for emitting into a surrounding formation a current I₀ via one ofthe annular electrodes, and a current I′₀ via the other annularelectrode;

an annular electrode for measuring potential, situated between the twocurrent electrodes, or else an array of azimuth electrodes situatedbetween the two annular current electrodes.

The tools of the prior art, and those described above, require thecurrent I₀ or the current I₀ and I′₀ as emitted from the annular currentelectrode(s) into the terrestrial formation to be focused. Means musttherefore be implemented for providing such focusing. In general, thisrequires a feedback loop to enable the focusing current(s) to beadjusted as a function, for example, of a signal representative of afocusing potential. In theory this implies amplification with infinitegain, but in practice gain must be limited in order to ensure stability.In particular, when using focusing potential measurement electrodes, asis usually the case, the result is that these electrodes are not atexactly the same potential and this gives rise to a measurement error.Although the error is very small, particularly in standard “DualLaterolog” type tools, it can become large when the spacing between thefocusing voltage measurement electrodes is reduced in order to improvethe resolution of the apparatus.

Consequently, it is desirable to be able to propose a method andapparatus for measuring the resistivity of drilling mud that enable theobjects already specified above to be achieved while also making itpossible to eliminate errors due to the presence of a feedback loop.

The invention thus also provides a method of measuring the resistivityof drilling mud in a borehole passing through a terrestrial formation,the method comprising:

inserting a sonde into the borehole, the sonde having an elongate bodyprovided with at least one annular current electrode and at least twoannular guard electrodes situated on either side of the annular currentelectrode;

performing computed focusing to simulate an operating mode in which:

at least one current I₀ is emitted into the surrounding formation fromthe annular current electrode;

the current I₀ is focused in the formation by emitting two currents I₁and I′₁ from the two annular guard electrodes situated on either side ofthe annular current electrode;

producing a signal representative of the resistivity R_(m) of thedrilling mud from the simulated operating mode.

This method does not require any direct focusing to be implemented, andit makes use only of focusing by computation. Since the stimulation isgenerally performed by computer apparatuses on the surface, themeasurement tool as used is considerably simplified. Also, insofar as nodirect focusing takes place during measurement, the means forcontrolling and/or regulating the focusing current are not implemented.This avoids all of the focusing current feedback loops.

In addition, this method does not require prior knowledge of the azimuthresistivity of the surrounding formations. It is less sensitive thanprior art methods to effects due to variations in the dimensions of theborehole.

In a particular implementation, the computed focusing may be performedon the basis of two real or “effective” operating modes of the sonde:

a first mode in which current having great penetration depth is emittedinto the surrounding formations; and

a second mode in which current having shallow penetration depth isemitted into the surrounding formations.

In the first mode, the currents of greater penetration depthsubsequently return to the surface. In contrast, in the second mode, thecurrents do not penetrate very far into the surrounding formations.

The computed focusing may be implemented on the basis of the twofollowing modes:

a first operating mode in which current is emitted into the surroundingformation, specifically a current i₁ from one of the annular guardelectrodes and a current i′₁ from the other annular guard electrode, thecurrent emitted by the annular current electrode(s) being equal to 0;

a second operating mode in which at least one current i₀ is emitted fromthe annular current electrode(s) to the annular guard electrodes, withthe total current emitted from the sonde into the formation being equalto 0.

In each mode, signals may be produced that are representative of a“focusing” voltage and of a “sonde” voltage; in addition, in the secondmode, a signal may be produced that is representative of the currentemitted from the current electrode(s).

In one computation technique, it is possible to deduce a weightingcoefficient from a linear combination of the two effective operatingmodes of the sonde so as to obtain a computed mode for which theresultant focusing voltage is zero.

In another computation technique, a signal is also produced in the firstmode that is representative of the total current emitted into theformation, and transfer impedances or coefficients are calculatedbetween:

firstly the focusing voltage and the sonde voltage; and

secondly the current emitted from the current electrode(s) and the totalcurrent emitted into the formation.

The measured value of R_(m) may then be deduced from the ratio of thesonde voltage value divided by the current value emitted from thecurrent electrode(s), for which values the focusing voltage is zero.

The sonde may comprise:

a single current electrode;

first, second, and third pairs of potential-measuring electrodesdisposed on either side of the current electrode;

the focusing voltage being equal to the difference V₁−V₂ between themean voltages from the first and second pairs of potential-measuringelectrodes;

the sonde voltage being equal to the difference V₂−V₃ between the meanvoltages from the second and third pairs of potential-measuringelectrodes.

In a variant, the sonde may comprise:

two annular current electrodes; and:

either an annular potential electrode disposed between the two currentelectrodes;

or else an array of azimuth electrodes disposed between the two currentelectrodes;

and first and second pairs of annular potential-measuring electrodes;

the focusing voltage being equal to the difference between the meanvoltage of the first pair of annular potential-measuring electrodes andeither the voltage of the annular potential electrode disposed betweenthe two current electrodes, or the mean voltage of the array of azimuthelectrodes;

the sonde voltage being equal to the difference between the meanvoltages of the first and second pairs of annular potential-measuringelectrodes.

The invention also provides an apparatus for measuring the resistivityof drilling mud in a borehole passing rough a terrestrial formation, theapparatus comprising:

a sonde having an elongate body provided with at least one annularcurrent electrode and at least two annular guard electrodes situated oneither side of the annular current electrode;

means for performing computed focusing so as to simulate an operatingmode in which:

at least one current I₀ is emitted into the surrounding formation fromthe annular current electrode;

the current I₀ is focused in the formation by emitting two currents I₁and I′₁ from the annular guard electrodes situated on either side of theannular current electrode;

means for computing a signal representative of the resistivity R_(m) ofthe drilling mud on the basis of the simulated operating mode.

This apparatus does not require means to be implemented for providingeffective control of focusing current. It therefore avoids any feedbackloop. In addition, it makes it possible to implement the abovedescribedmethod, with all of the corresponding advantages.

The sonde may also include means for use in a first effective operatingmode to emit currents of great penetration depth into the surroundingformations, and in a second effective operation mode for emittingcurrents of small penetration depth into the surrounding formations,with the means for performing computed focusing performing the focusingon the basis of these two effective modes of operation.

Thus, the sonde may comprise:

means for emitting into the surrounding formation in a first effectiveoperating mode both a current i₁ from one of the annular guardelectrodes and a current i′₁ from the other annular guard electrode, thecurrent emitted from the annular current electrode(s) being equal to 0;

means for emitting, in a second effective operating mode, at least onecurrent i₀ from the annular current electrode(s) to the annular guardelectrodes, the total current emitted from the sonde into the formationbeing equal to 0;

the means for performing computed focusing operating on the basis ofthese two effective operating modes.

Means may be provided to produce:

signals representative of a focusing voltage and of a sonde voltage;

a signal representative of the current(s) emitted from the currentelectrode(s).

In order to implement a first computation technique, in a firstembodiment, the means for performing computed focusing enable aweighting coefficient to be deduced from a linear combination of the twoeffective operating modes of the sonde, and to obtain a computed modefor which the resultant focusing voltage is zero.

In order to implement another computation technique, in anotherembodiment, means may be provided for use in the first effectiveoperating mode to produce a signal representative of the total currentemitted into the formation, the means for performing computed focusingserving to deduce transfer impedances or coefficients between:

means being provided for producing in the first effective operatingmode, a signal representative of the total current emitted into theformation;

the means for performing computed focusing enabling transfer impedancesor coefficients to be deduced between:

firstly the focusing voltage and the sonde voltage; and

secondly the current emitted from the current electrode(s) and the totalcurrent emitted into the formation.

The means for computing a signal representative of the resistivity R_(m)may be suitable for deducing R_(m) from the ratio of the sonde voltagevalue divided by the value of the current emitted from the currentelectrode(s), for which values the focusing voltage is zero.

The methods described above may also include a step of correcting themeasured values R_(m) to take account of the following sources of error

the highly resistive nature of the surrounding formation;

the presence of one or more highly conductive beds in the formation;

the influence of the borehole.

These corrections may, for example, be implemented by means of anextended Kalman filter.

The corresponding apparatuses may include corresponding means forimplementing the corrections.

BRIEF DESCRIPTION OF THE DRAWINGS

In any event, the characteristics and advantages of the invention appearmore clearly in the light of the following description. The descriptionrelates to embodiments given in non-limiting manner for explanatorypurposes, and it refers to the accompanying drawings, in which:

FIG. 1 shows logging apparatus including a sonde on which electrodes aredisposed for measuring the resistivity of drilling mud in accordancewith the invention;

FIGS. 2A and 2B show respectively a first embodiment of apparatus of thepresent invention, and a variant of the first embodiment, in a borehole;

FIG. 3 shows a second embodiment of apparatus of the present invention;

FIG. 4 shows a third embodiment of apparatus of the present invention;

FIGS. 5A and 5B show respectively a fourth embodiment of apparatus ofthe present invention and a variant of said fourth embodiment in aborehole;

FIGS. 6A and 6B are electrical circuit diagrams for implementing amethod and apparatus of the invention for direct focusing;

FIGS. 7A to 7C are diagrams showing effective operating modes that canbe used when implementing a method of the present invention that makesuse of computed focusing, and also showing the mode that results fromcombining the two effective modes;

FIG. 8 is an electronic circuit diagram for implementing a method of thepresent invention that makes use of computed focusing; and

FIG. 9 shows the influence of the characteristics of the borehole on mudresistivity measurements performed in accordance with the invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Overall implementation of the invention is initially showndiagrammatically in FIG. 1 where there can be seen logging apparatusenabling the characteristics of terrestrial formations 11 surrounding awell or borehole 10 to be determined. The apparatus comprises a sonde 12which is suspended down the borehole at the end of a multiconductorcable 13. The cable 13 passes over a sheath 14 and is wound on a drum 15which serves to move the sonde 12 along the borehole. The drum 15 formspart of a surface unit 16 which may also include means for computerprocessing data measured by the sonde while it is being displaced in theborehole.

The sonde 12 is elongate in shape. It comprises a body 17 having a topportion 20 made of a metal case enclosing electrical circuits, and abottom portion 21 in which devices for measuring the formations 11 maybe included. In addition, the section 21 has an array 22 of electrodesmaking it possible, in particular, to determine the resistivity of thedrilling mud.

One such array 22 of electrodes is described below in the context of afirst embodiment and with reference to FIG. 2A.

This figure is a diagrammatic representation of the array of electrodeson its own, i.e. without the body of the sonde. First, second and thirdpairs of annular potential-measuring electrodes (M₁, M′₁,; M₂, M′₂; M₃,M′₃) are disposed on either side of a central annular electrode A₀, alsoreferred to as a “current” electrode. The electrode M₃ is disposedbetween M₁ and M₂ (and likewise M′₃ between M′₁ and M′₂). On either sideof this assembly, there are disposed two annular electrodes A and A′,also referred to as “guard” electrodes. A current I₀ is emitted by theelectrode A₀, which current passes through the drilling mud and then theterrestrial formations, after which it returns to the surface. CurrentsI and I′ are emitted into the same formations from the guard electrodesA and A′. These currents are also referred to as “focusing” currents:they serve to keep the current I₀ in a narrow slice of groundperpendicular to the axis of the apparatus. In order to be able tomaintain the magnitudes of the currents I and I′ at values that enablegood focusing to be ensured, the annular potential-measuring electrodesserve to obtain a signal representative of a focusing potential; thisapplies in particular to electrode pairs M₁, M′₁ and M₂, M′₂: the meanvoltage V₁ of electrode pair M₁ M′₁ and the mean voltage V₂ of electrodepair M₂, M′₂ are both measured, or else a signal or signalsrepresentative of these voltages are produced. The condition forfocusing is then written: V₁=V₂. The currents I and I′ are adjusted soas to ensure that this condition is satisfied. An electrical circuit foradjusting the currents I and I′ as a function of this condition isdescribed below.

Also, although the current I₀ is emitted perpendicularly to the sondeinto the drilling mud and towards the formation, it nevertheless inducesvoltages in the drilling mud. Such voltages can be measured; inparticular, a signal representative of an induced voltage may beproduced, e.g. by measuring the mean voltage of a pair of annularelectrodes, such as the pair M₃, M′₃, and by comparing said mean voltagewith the mean voltage V₁. More precisely, the resistivity of the mudR_(m) is written: $R_{m} = {K\frac{V_{1} - V_{3}}{I_{0}}}$

where K is a factor that depends on the geometry of the sonde.

Because of the focusing, the path of the current I₀ in the column of mudis stable and independent of the resistivity of the formation locatedbeyond the column of mud, providing the hole is not too small.

With the method of the invention, the current I₀ is sent into theterrestrial formation, and it is with this current that R_(m) ismeasured and not with a superficial current, i.e. a current flowingessentially in the drilling mud.

In a variant, which makes it possible for a sonde used in apparatus ofthe invention to be made compatible with sondes used for othermeasurements, the guard electrodes A and A′ may be split into twoportions A₁, A₂ (for electrode A) and A′₁, A′₂ (for electrode A′), asshown in FIG. 2B. It is convenient to add an annular potential-measuringelectrode A₁ * adjacent to the electrode A₁ (and A₁ *′ adjacent to A′₁).The focusing current I is then emitted by the electrodes A₁ and A₂ whichare maintained at the same potential (and likewise I′ by A′₁ and A′₂).The other electrodes (the annular potential-measuring electrodes and thecentral current electrode A₀) of the electrode structure in FIG. 2B areidentical to those of FIG. 2A. FIG. 2B also shows, diagrammatically, therelative disposition of the set of electrodes, the borehole 10, and theformation 11. The figure also shows current lines for the current I₀ andthe focusing currents I and I′. In the figure, it can be seen clearlythat the current I₀ remains, over a certain distance, within a sliceperpendicular to the axis of the hole 10. At infinity, the current I₀returns to the surface. The current lines obtained would besubstantially the same with electrodes organized as shown in FIG. 2A,where the guard electrodes are not split in two.

Another arrangement of electrodes for a sonde for use in apparatus ofthe invention is now described with reference to FIG. 3. This structuremakes use of two annular current electrodes A₀ and A′₀. On either sideof this assembly there are two pairs of annular potential-measuringelectrodes M₁, M′₁ and M₃, M′₃. Between the two annular currentelectrodes A₀ and A′₀, there is an annular potential-measuring electrodeM₀. At the ends, on either side of the above assembly, there are twoguard electrodes A and A′. An investigation current I₀ is emitted byannular current electrode A₀ (and I′₀ by A′₀). The guard electrodes emitfocusing currents I and I′. Here again, the currents I₀ and I′₀ areemitted towards the formation, pass through it, and return to theearth's surface at infinity. Because they have passed through thedrilling mud, they establish voltages therein, and a voltage in thedrilling mud can be measured, e.g. between electrode pairs M₁, M′₁ andM₃, M′₃. The resistivity of the mud is then obtained by the formula:$R_{m} = {K^{\prime}\frac{V_{1} - V_{3}}{I_{0} + I_{0}^{\prime}}}$

where V₁ designates the mean potential of electrode pair M₁, M′₁, (andV₃ of pair M₃, M′₃). The condition for proper focusing of the currentsI₀ and I₀ by the currents

I and I′ is written:

V₁=V₀

where V₁ has the same meaning as above and V₀ is the potential of theelectrode M₀.

For the same reasons as those already given above (compatibility withelectrode structures used for other measurements) the guard electrodesmay be split in two in this case also, in the manner explained withreference to FIG. 2B.

Another embodiment of an electrode structure suitable for use inapparatus for implementing the invention is described below withreference to FIG. 4. In this figure, elements that are identical to orthat correspond to items described above with reference to FIG. 3 aregiven the same references. Compared with the FIG. 3 structure, theelectrodes M₃, M′₃ have been omitted. Instead, an annularpotential-measuring electrode A₀* is disposed in the middle of currentelectrode A₀, i.e. one portion of A₀ extends above an annularpotential-measuring electrode A₀* while another portion of the sameelectrode A₀ extends below A₀*. The same disposition is adopted for A′₀and an electrode A₀*′, which electrode likewise acts as an annularpotential-measuring electrode. Investigation currents I₀ and I′₀ areemitted through the drilling mud towards the formation. They are focusedby the currents I and I′, in the same manner as for the electrodestructure described above with reference to FIG. 3. The resistivity ofthe drilling mud is measured in application of the formula:$R_{m} = {K_{1}\frac{V_{0}^{*} - V_{0}}{I_{0} + I_{0}^{\prime}}}$

where V₀* designates the mean potential of the electrodes A₀* and A₀*′.The condition for focusing is written: V₁=V₀, where V₁ and V₀ have thesame meanings as given above.

In principle, the apparatus of FIG. 4 operates in the same manner asthat of FIG. 3. Inserting a potential-measuring electrode between twoportions of a current electrode makes it possible to improve certainmeasurements when contact impedance variations occur at the surface ofelectrode A₀ or A′₀.

In a variant of this embodiment, it is possible to place the pair ofannular potential-measuring electrodes A₀* and A₀*′ between thecorresponding current electrodes A₀, A′₀ and the annularpotential-measuring electrode M₀. The formulas given above in thedescription of FIG. 4 apply in this case also.

Another embodiment of an electrode structure that can be implemented inthe context of the present invention is shown in FIG. 5A. This structureis derived from the structure of FIG. 4 by replacing the central annularvoltage-measuring electrode M₀ by an array of N azimuth electrodesA_(azi). Here again, the resulting structure is compatible withelectrode structures otherwise used for other measurements. An array ofazimuth electrodes is used, in particular, for performing measurementsin different directions around the sonde, in particular measurements ofazimuth resistivity. Investigation currents I₀ and I′₀ are emitted bythe annular electrodes A₀ and A′₀ and they are focused by currents I andI′ respectively emitted by electrodes A and A′. The envelope of currentlines is represented diagrammatically in FIG. 5B for an electrodestructure that corresponds essentially to that of FIG. 5A. A differencelies in the guard electrodes being spilt into two portions as explainedabove with reference to FIG. 2B, thereby obtaining the same advantages.References identical to those used in that figure designate the sameelements in the present figure.

The resistivity of the mud is then given by:$R_{m} = {K_{1}^{\prime}\frac{V_{0}^{*} - V_{zi}}{I_{0} + I_{0}^{\prime}}}$

where V₀* represents the mean potential of the electrodes A₀* and A₀*′,while V_(zi) represents the mean potential of the array of azimuthelectrodes. Also, the condition for focusing is written: V₁=V_(zi),where V₁ represents the mean potential of the electrodes M₁ and M′₁.

FIG. 6A is an electrical circuit diagram for use with an electrodestructure of the invention, for the particular case of the structureshown in FIG. 2A. A generator 30, e.g. situated on the surface, deliversa current which is transmitted via a cable 32 to the electrodes A and A′each of which emits a focusing current, and to the electrode A₀ whichemits an investigation current I₀. Means may be provided for measuringthe total generated current, e.g. by placing a resistor 34 so thatvoltage can be taken from across its terminals and applied to adifferential amplifier 36 and to current calculating means 38, forexample. Means are also provided for measuring the current I₀, forexample voltages are taken from the terminals of a resistor 40 and areapplied to a differential amplifier 42. The focusing voltage controlloop (between electrode pairs M₁, M′₁, and M₂, M′₂) serves to take thevoltages from the terminals of the electrodes to measure the focusingpotential, which voltages are transmitted to differential amplifiers 44and 46 whose outputs are connected to the inputs of a summing circuit48. The output of the summing circuit is amplified (amplifier 50) and,if there is unbalance relative to the focusing condition (whichcondition is written V₁=V₂), a non-zero signal is delivered to atransformer 52 which then controls a different distribution of currentsamongst the annular guard and current electrodes. The measured currentI₀ is transmitted from the output of amplifier 42 to a multiplexer 54which is followed by an analog-to-digital converter 56, a digitalprocessor 58, and a telemetry emitter 60. The signal is then transmittedto the surface via the cable 32.

The measurement signal is obtained from signals taken from the terminalsof electrodes pairs M₁, M′₁ and M₃, M′₃, which signals are transmittedto differential amplifiers 62 and 64 whose outputs are delivered to asumming circuit 66. The resulting signal is filtered by a bandpassfilter 68 and is transmitted to the multiplexer 54 which is followed bythe above-described elements 56, 58, and 60. The resulting signal istransmitted to the surface.

An electrical circuit diagram for ensuring equal potentials onelectrodes A₁ and A₂ of FIG. 2B, for example, is given in FIG. 6B. Inthis figure, only the top portion of the sonde above electrode A₀ isshown. An electrode A₁* is associated with electrode A₁ so as to make itpossible to measure the potential of A₁. An amplifier 70 delivers asignal proportional to the voltage measured between electrode A₂ andelectrode A₁*. A differential amplifier 72 compares the resulting signalwith ground potential. If there is unbalance between the voltages ofelectrodes A₂ and A₁*, then amplifier 72 delivers a non-zero signal to atransformer 74 which then controls a different distribution of currentsbetween electrodes A₁ and A_(2.) The same circuit can be applied toelectrodes A′₁ and A′₂, electrode A′₁ being associated with apotential-measuring electrode A₁*′. All of the elements 70 to 76 may beintegrated in the body of the sonde lowered down the borehole.

The tools or electrode arrangements for a sonde as described above arefor implementing a method that makes use of direct or effective focusingof the investigation current in the surrounding formations. It is alsopossible to perform computed focusing, i.e. focusing that is simulatedon the basis of effective modes that do not make use of direct focusing.All of the electrode arrangements that have been described above can beused to implement computed focusing, the overall apparatus includingmeans specific to implementing such computed focusing.

The principle of computed focusing in the particular case of measuringmud resistivity is described briefly with reference to FIGS. 7A to 7C.In these figures, the arrangement of electrodes taken into considerationis identical to that described above with reference to FIG. 5B, howeverthis is not limiting.

The sonde enables two effective modes of operation to be performed:

a first mode (FIG. 7A) in which currents are emitted that haveconsiderable penetration depth into the surrounding formations; forexample, a current i₁ is emitted into the formations from a first set ofannular guard electrodes, and a current i′₁ is emitted from the otherset of annular guard electrodes, with the current emitted by the annularcurrent electrodes being equal to 0; and

a second mode (FIG. 7B) in which currents are emitted that have shallowpenetration depth into the surrounding formations; for example, currentsi₀ and i′₀ are emitted from the annular current electrodes to theannular guard electrodes, with the total current emitted from the sondeinto the formation being equal to 0.

Both of the above modes may be implemented simultaneously but atdifferent frequencies, with the first mode being implemented at 35 Hz,for example, while the second mode is implemented at about 162 Hz. Ifthe selected frequencies are equal or close together, then the twoeffective modes of operation need to be implemented successively.

While operating in these modes, signals representative of a focusingvoltage and signals representative of a sonde voltage may be taken andmeasured. A signal representative of the resistivity R_(m) of thedrilling mud is deduced by simulation after reconstruction of a focusedmode of operation.

Thus, it is possible to compute which respective weights should be givento the two effective operating modes so that a linear combinationthereof provides an operating mode in which the condition for focusingis satisfied. Such a mode is shown in FIG. 7C: it can be seen that thesame current lines are associated therewith as when effectivelyoperating with direct focusing, as shown in FIG. 2B.

In a variant, it is possible to use the data measured during theeffective operating modes to compute transfer impedances which enablethe investigation currents and the total currents emitted into theformation to be associated with a focusing potential and with a sondepotential. After these transfer impedances have been computed, it ispossible to deduce therefrom voltage values for the sonde andinvestigation current values for which a focusing condition issatisfied.

In general, it is considered that an operating mode, whether effectiveor simulated, is completely described by the data of the investigationcurrent(s), the total current emitted in the formation, a focusingvoltage, and a sonde voltage. When the annular guard electrodes aresplit into two portions (as shown in FIGS. 7A to 7C), the value of thevoltage difference between electrodes A₁ and A₂, and also betweenelectrodes A′₁ and A′₂ does not have any effect since this voltagedifference is kept at zero.

In the structure of FIG. 2A, the focusing voltage may be given by thedifference V₂−V₁, whereas the probe voltage is given by the differenceV₃−V₁.

In the structure of FIG. 3, the focusing voltage is the voltage V₁−V₀,an the tool voltage is the difference V₃−V₁.

In the structure shown in FIG. 4, the focusing voltage is equal toV₁−V₀, while the sonde voltage is equal to V₁−V₀*.

In the electrode structure shown in FIGS. 5A and 5B, the focusingvoltage is the voltage V₁−V_(zi) and the sonde voltage is equal toV₁−V₀*.

The first computation technique is now described in greater detail. Foreach mode, the investigation current is written I₀, the sonde voltageΔV_(m), and the focusing voltage ΔV_(m).

The notation I_(0,i,)ΔV_(0,i,)ΔV_(m,i) is used for the correspondingquantities in mode No. i (i=1, 2 or d, where d is the index for computedmode, with the mode i being described by the following column vector:$\begin{pmatrix}{\Delta \quad V_{0,1}} \\{\Delta \quad V_{m,i}} \\I_{0,i}\end{pmatrix}$

The computed focusing condition is written: ΔV_(m,d)=0, and theweighting of the two modes is designated by the coefficient λ. It istherefore necessary to find λ such that: ${{\lambda \begin{pmatrix}{\Delta \quad V_{0,i}} \\{\Delta \quad V_{m,i}} \\I_{0,i}\end{pmatrix}}\quad + \begin{pmatrix}{\Delta \quad V_{0,2}} \\{\Delta \quad V_{m,2}} \\I_{0,2}\end{pmatrix}}\quad = \quad \begin{pmatrix}{\Delta \quad V_{0,d}} \\0 \\I_{0,d}\end{pmatrix}$

This equality is satisfied for:$\lambda = \frac{\Delta \quad V_{m,2}}{\Delta \quad V_{m,1}}$

from which it can be deduced:${\Delta \quad V_{0,d}} = {{{- \left( \frac{\Delta \quad V_{m,3}}{\Delta \quad V_{m,1}} \right)}\Delta \quad V_{0,1}} + {\Delta \quad V_{0,2}}}$and $I_{o,d} = {{{{- \begin{pmatrix}{\Delta \quad V_{m,3}} \\{\Delta \quad V_{m,1}}\end{pmatrix}}I_{0,1}} + I_{0,2}} = I_{0,2}}$

With the resistivity of the mud being deduced therefrom as follows:$R_{m} = {{\left( \frac{\Delta \quad V_{0,d}}{I_{0,d}} \right)K^{''}} = {K^{''} \times \frac{{\Delta \quad {V0}},{2 - \left( {{\Delta \quad {V0}},{1\frac{\Delta \quad V_{m,2}}{\Delta \quad V_{m,1}}}} \right.}}{I_{0,2}}}}$

where K″ is a coefficient which depends on the geometricalcharacteristics of the sonde.

The data obtained on the voltages and the currents from the effectivemodes may be measured and then stored, for example. The coefficient λand the resistivity of the mud are computed subsequently, e.g. by meansof a known type of computer that is specially programmed to perform thistype of computation. By way of example, the computer may be contained inthe surface unit 16 (see FIG. 1).

In another computation technique, a matrix A is initially computedenabling the vectors V and I to be associated by the relationship: V=A.Iwhere $V = \begin{pmatrix}{\Delta \quad V_{m}} \\{\Delta \quad V_{0}}\end{pmatrix}$ and $I = \begin{pmatrix}I_{0} \\I_{1}\end{pmatrix}$

A is a 2′2 matrix whose coefficients are written as follows:$A = \begin{pmatrix}a & b \\d & e\end{pmatrix}$

From the two effective modes, the following four equations are thusobtained:

ΔV_(m,1)=bI_(t,1)

ΔV_(0,1)−eI_(t,1)

 ΔV_(m,2)=aI_(0,2)

ΔV_(0,2)=dI_(0,2)

from which it is possible to deduce the four coefficients or transferimpedances a, b, c, e.

The condition for focusing is written: ΔV_(m,d)=0. It therefore sufficesto find voltages ΔV₀ and currents I₀ which satisfy: $\begin{pmatrix}0 \\{\Delta \quad V_{0,4}}\end{pmatrix} = {{\begin{pmatrix}a & b \\c & e\end{pmatrix}\begin{pmatrix}I_{0} \\I_{1}\end{pmatrix}} = {A\begin{pmatrix}I_{0} \\I_{1}\end{pmatrix}}}$

The resistivity of the mud is deduced therefrom as follows:

R_(m)=K″.(ΔV_(0,d)/I_(0,d))=K″(d−e(a/b))

By replacing the transfer impedances by the values obtained from thevoltages and the currents measured in the effective modes, the sameexpression is obtained as in the first equality given above for R_(m).

This technique requires the measured values of the currents and of thevoltages for the effective modes to be stored, after which a step ofcomputing the transfer impedances is performed. The computation may beperformed by a computer of known type, programmed appropriately forperforming this type of computation.

FIG. 8 is an electrical circuit for use in a sonde in the context of amethod of the invention for measuring mud resistivity by computedfocusing. The electrode structure concerned is that described above withreference to FIG. 2A. A current source 80, e.g. situated at the surface,delivers a total current I_(t) for enabling the sonde to operate in thefirst effective mode. This current is delivered via a cable 82. Meansare provided (resistor 84, amplifier 86, phase measuring circuit 88) formeasuring the phase of the current I_(t). The current I₀ (when operatingin the second effective mode) is produced by a generator 90 driven by adigital processor 92, a digital-to-analog converter 94, and a lowpassfilter 96. The focusing voltage is obtained by means of differentialamplifiers 98 and 100 that take the difference between and amplify thevoltages from annular electrode pairs M₂, M₃ and M′₂, M′₃. The signalsfrom the differential amplifiers are applied to a summing circuit 104whose output signal is filtered (bandpass filter 106) and is thenapplied to a multiplexer 108. The signals for measuring the voltage ofthe sonde are formed by differential amplifiers 110 and 112 whichamplify and take the difference between the voltages from electrodepairs M₁, M₃ and M′₁, M′₃. The resulting signals are applied to asumming circuit 114 whose output is then filtered (bandpass filter 116),which signal is subsequently applied to the multiplexer 108. Themultiplexer is connected to an analog-to-digital converter 118 in turnconnected to the digital processor 92. The signal is then applied to atransmitter 120. The apparatus also includes a receiver 122 and acomputer 124.

In all cases, whatever the measurement technique used (direct focusingor computed focusing), the measured resistivity of the mud may besubject to three sources of error:

if the formation surrounding the borehole is very resistive, then thecurrent I₀ (investigation current) is very low, so the measured signalsare low and the signal/noise ratio decreases;

if a zone or bed in a formation is particularly conductive, then theinvestigation current travels in part towards said conductive zone evenif it is not situated facing the current electrode(s); and

in small diameter holes of low contrast, or when the sonde is highlyeccentric within the hole, then the influence of the hole is alsoperceptible.

These effects can be corrected in real time, e.g. by a processing methodrelying on the use of an extended Kalman filter. This method consists initeratively solving two equations, for each depth a at which ameasurement is performed:

hrmd(n)=f[rm(n),hlld(n),dh(n),ec(n)]+ε(n)  (1)

rm(n)=rm(n−1)+δ(n)  (2)

The first equation (1) is the measurement equation at depth n, in which:

hrmd is the raw measurement obtained using the sonde of the resistivityof the mud;

f is the direct model of the measurement, expressed as a function:

of the measured resistivity of the formation hlld(n);

of the resistivity of the mud rm(n);

of the diameter of the hole, dh(n); and

of the eccentricity of the sonde in the hole ec(n).

The function ε is a stochastic parameter or random variable representingnoise in measurement and uncertainty for f.

The second equation (2) represents variation in mud resistivity withdepth. δ(n) is a random variable taking account of the dynamics.

The variance of ε is evaluated and adjusted at each depth level as afunction of the measurement variance. Thus, if there are highlyresistive beds, then ε takes on very large values. This gives risemathematically to greater weight being given to the second equation. Inwhich case, the last good estimate rm of R_(m) (or an extrapolationtherefrom) is retained. The hole effect is modelled and corrected by thefirst equation.

At each depth n, f is computed and compared with the raw measurementhrmd.

Equations (1) and (2) are solved by finding the most probable value{circumflex over (rm)} (n). Assuming that ε (n) and δ (n) are Gaussian,that amounts to maximizing a non-linear cost function that representsthe weighed sum of reconstruction error [hrmd(n)−f({circumflex over(rm)} (n) . . . )]² and the a priori error [rm(n−1)−{circumflex over(rm)} (n)]². The solution can be found by the Gauss-Newton method.

The correction method described above can be implemented by means of aconventional computer programmed in appropriate manner. The correctionsmay be performed on the surface close to the borehole, or remotely afterthe measurement data has been transferred.

The results obtained by finite element modelling of the response areillustrated in FIG. 9. This figure shows how the ratio rm/f (correctionfactor) varies as a function of R_(t)/R_(m), i.e. as a function of theratio of formation resistivity to mud resistivity, or in other words asa function of the contrast between the resistivity and the mud. Curve Iis plotted for a hole diameter of 12.5 cm, curve II for a hole diameterof 15 cm, and substantially superposed curves m, IV, and V correspond torespective hole diameters of 20 cm, 30 cm, and 40 cm. Formationresistivity continues to have an influence in small diameter holes, e.g.an influence of about 15% when the hole diameter is about 15 cm. Inholes of larger diameter, the influence of formation resistivity rapidlybecomes very small and is negligible when the hole diameter is greaterthan 20 cm. The curves in FIG. 9 were obtained for a centered tool, i.e.eccentricity has no effect.

What is claimed is:
 1. A method of measuring the resistivity of drillingmud in a borehole (10) passing through a terrestrial formation, themethod comprising: inserting a sonde (12) into the borehole, the sondehaving an elongate body (17) provided with at least one annular currentelectrode (A₀, A′₀) and at least two annular guard electrodes (A, A′,A₁, A′₁, A₂, A′₂) situated on either side of the annular currentelectrode; performing computed focusing to simulate an operating mode inwhich: at least one current I₀ is emitted into the surrounding formationfrom the annular current electrode; the current I₀ is focused in theformation by emitting two currents I₁ and I′₁ from the two annular guardelectrodes situated on either side of the annular current electrode;producing a signal representative of the resistivity R_(m) of thedrilling mud from the computed focusing.
 2. A method according to claim1, computed focusing being implemented from two effective operatingmodes of the sonde: a first mode in which current having greatpenetration depth is emitted into the surrounding formations; and asecond mode in which current having shallow penetration depth is emittedinto the surrounding formations.
 3. A method according to claim 1,computed focusing being performed on the basis of two effectiveoperating modes of the sonde: a first operating mode in which current isemitted into the surrounding formation, specifically a current i₁ fromone of the annular guard electrodes and a current i′₁ from the otherannular guard electrode, the current emitted by the annular currentelectrode(s) being equal to 0; a second operating mode in which at leastone current i₀ is emitted from the annular current electrode(s) to theannular guard electrodes, with the total current emitted from the sondeinto the formation being equal to
 0. 4. A method according to claim 2,in which, for each mode, signals are produced representative of afocusing voltage and of a sonde voltage; and in which a signal isproduced for the second mode representative of the current(s) emittedfrom the current electrode(s).
 5. A method according to claim 4, inwhich a weighting coefficient is deduced for a linear combination of thetwo effective operating modes of the sonde so as to obtain a computedmode for which the resulting focusing voltage is zero.
 6. A methodaccording to claim 4, in which there is also produced, for the firstmode, a signal representative of the total current emitted into theformation, and in which transfer impedances or coefficients are deducedbetween: firstly the focusing voltage and the sonde voltage; andsecondly the current emitted from the current electrode(s) and the totalcurrent emitted into the formation.
 7. A method according to claim 4,the measurement of R_(m) being deduced from the ratio of the value ofthe sonde voltage divided by the value of the current emitted from thecurrent electrode(s), for which values the focusing voltage is zero. 8.A method according to claim 4, the sonde comprising: a single currentelectrode (A₀); first, second, and third pairs of potential-measuringelectrodes (M₁, M′₁; M₂, M′₂; M₃, M′₃) disposed on either side of thecurrent electrode; the focusing voltage being equal to the differenceV₁−V₂ between the mean voltages from the first and second pairs ofpotential-measuring electrodes (M₁, M′₁; M₂, M′₂); the sonde voltagebeing equal to the difference V₂−V₃ between the mean voltages from thesecond and third pairs of potential-measuring electrodes (M₂, M′₂; M₃,M′₃).
 9. A method according to claim 4, the sonde comprising: twoannular current electrodes (A₀, A′₀); and: either an annular potentialelectrode (M₀) disposed between the two current electrodes; or else anarray of azimuth electrodes (A_(azi)) disposed between the two currentelectrodes; and first and second pairs of annular potential-measuringelectrodes (M₁, M′₁, M₃, M′₃, A₀*, A₀*′); the focusing voltage beingequal to the difference between the mean voltage of the first pair ofannular potential-measuring electrodes (M₁, M′₁) and either the voltageof the annular potential electrode (M₀) disposed between the two currentelectrodes, or the mean voltage of the array of azimuth electrodes(A_(azi)); the sonde voltage being equal to the difference between themean voltages of the first and second pairs of annularpotential-measuring electrodes.
 10. A method according to claim 1,further including a step of correcting the measured values to takeaccount of at least the following sources of error: the highly resistivenature of the surrounding formation; the presence of one or more highlyconductive beds in the formation; the influence of the borehole.
 11. Amethod according to claim 10, in which the correction step implements anextended Kalman filter.
 12. Apparatus for measuring the resistivity ofdrilling mud in a borehole (10) passing through a terrestrial formation(11), the apparatus comprising: a sonde (12) having an elongate body(17) provided with at least one annular current electrode (A₀, A′₀) andat least two annular guard electrodes (A, A′, A₁, A′₁, A₂, A′₂) situatedon either side of the annular current electrode; means for performingcomputed focusing so as to simulate an operating mode in which: at leastone current I₀ is emitted into the surrounding formation from theannular current electrode (A₀, A′₀); the current I₀ is focused in theformation by emitting two currents I₁ and I′₁ from the annular guardelectrodes situated on either side of the annular current electrode;means for computing a signal representative of the resistivity R_(m) ofthe drilling mud on the basis of the computed focusing.
 13. Apparatusaccording to claim 12, the sonde further comprising means for emittingin a first effective operating mode currents having great penetrationdepth in the surrounding formations and, in a second effective operatingmode, currents having shallow penetration depth into the surroundingformations; the means for performing computed focusing operating on thebasis of these two effective operating modes.
 14. Apparatus according toclaim 12, the sonde including: means for emitting into the surroundingformation in a first effective operating mode both a current i₁ from oneof the annular guard electrodes and a current i′₁ from the other annularguard electrode, the current emitted from the annular currentelectrode(s) being equal to 0; means for emitting, in a second effectiveoperating mode, at least one current i₀ from the annular currentelectrode(s) to the annular guard electrodes, the total current emittedfrom the sonde into the formation being equal to 0; the means forperforming computed focusing operating on the basis of these twoeffective operating modes.
 15. Apparatus according to claim 13, meansbeing provided for producing, in each mode: signals representative of afocusing voltage and of a sonde voltage; a signal representative of thecurrent(s) emitted from the current electrode(s).
 16. Apparatusaccording to claim 15, the means for performing computed focusingenabling a weighting coefficient to be deduced for a linear combinationof the two effective operating modes of the sonde, and for obtaining acomputed mode in which the resulting focusing voltage is zero. 17.Apparatus according to claim 15, means being provided for producing inthe first effective operating mode, a signal representative of the totalcurrent emitted into the formation; the means for performing computedfocusing enabling transfer impedances or coefficients to be deducedbetween: firstly the focusing voltage and the sonde voltage; andsecondly the current emitted from the current electrode(s) and the totalcurrent emitted into the formation.
 18. Apparatus according to claim 17,the means for computing a signal representative of the resistivity R_(m)being suitable for deducing R_(m) from the ratio of the value of thesonde voltage divided by the value of the current emitted from thecurrent electrode(s), values for which the focusing voltage is zero. 19.Apparatus according to claim 15, the sonde comprising: a single currentelectrode (A₀); first, second, and third pairs of potential-measuringelectrodes (M₁, M′₁; M₂, M′₂; M₃, M′₃) disposed on either side of thecurrent electrode.
 20. Apparatus according to claim 15, the sondecomprising: two annular current electrodes (A₀, A′₀), and: either anannular potential electrode (M0) disposed between the two currentelectrodes; or else an array of azimuth electrodes (A_(azi)) disposedbetween the two current electrodes; and first and second pairs ofannular potential-measuring electrodes (M₁, M′₁; A₀*, A₀*′), one of thetwo pairs (M₁, M′₁) being situated on either side of the annular currentelectrodes.
 21. Apparatus according to claim 12, further including meanssuitable for performing correction on the measured values in order totake account at least of the following sources of error: the highlyresistive nature of the surrounding formation; the presence of one ormore highly conductive beds in the formation; the influence of theborehole.
 22. Apparatus according to claim 12, further including meanssuitable for performing correction on the measured values in order totake account at least of the following sources of error: the highlyresistive nature of the surrounding formation; the presence of one ormore highly conductive beds in the formation; the influence of theborehole.